Roman Kogan

Roman Kogan
Research Scholar
Geometric Group Theory
This user account status is Approved

This user has not added any information to their profile yet.

My research is currently focused on Mealy automata and their Schreier graphs. There are two projects I am working on, as a continuation of my PhD thesis [1]:

1. Given a Markov measure µ, what is its pushforward g ? µ by the action of a finite-state automaton? When are µ and g ? µ singular? When is g ? µ Gibbsian? (The question was explored for Bernoulli measures by R. Kravchenko). This question is answered fully for the case when g is invertible in our upcoming paper with R. Grigorchuk and V. Vorobets using the machinery related to the project below.

2. Given a transitive action of a Mealy machine A on the standard binary tree, one can, for a Mealy machine B consider the distribution of (directed graph) distances by which the vertices of the tree on a given level are moved by B in the cycle generated by the action of A. This leads to the definition of an interesting function, the automatic logarithm, and in some cases, gives rise to a shift-invariant measure (suggested by Y. Vorobets) with interesting properties.

Further research interests involve applying automata theory to groups - in particular, the Thompson groups F, T and V , and their n-dimensional generalizations nV introduced by Brin in [2]. The question of whether F is an automaton group is still open.

While the conjugacy problem for F has been solved (in a particularly nice way by Belk in [3]with strand diagrams), it is still open for nV .

I wrote software for computation in nV ([4]), and plan to port it to GAP for a wider audience


To learn more, visit:

Check out Roman's music at

Contact Roman at roman /dot/ kogan at-sign ronininstitute dot org